Analysis Of The Forces Acted On The Inner Cylinder By Power Law Fluid Flowing In Annulus With The Inner Cylinder Executing A Planetary Motion

Under the behavior of production by screw pump, the pump rod rotates not only around its own axis but also around the axis of the oil tube, for the effects of its self-weight and decentralization. The flow of produced liquid in annulus formed by the pump rod and the oil tube could be regarded as flow of non-Newtonian fluid in annulus with the inner cylinder executing a planetary motion. So research on the forces acted on the inner cylinder by non-Newtonian fluid flowing in annulus with the inner cylinder executing a planetary motion is of certain theoretical instruction significance for analyzing and controlling eccentric wear and break of pump rod, optimizing and designing the parameters of pump in screw pump production well.In this paper, the rheological properties of the produced liquid in screw pump production well are described by the model of power law fluid. The mathematical models of the forces acted on the inner cylinder by non-Newtonian fluid flowing in annulus with the inner cylinder executing a planetary motion are established. The calculation formulas of normal stress difference, tangential stress and moment acted on the inner cylinder by the fluid are given, and the numerical solutions of them are obtained by finite difference method. The effects of the rotation and revolution velocities of the inner cylinder, the eccentricity and the pressure gradient on the normal stress difference, tangential stress and moment acted on the inner cylinder are analyzed respectively when Newtonian and power law fluid flow in annulus with the inner cylinder executing a planetary motion. And the results indicate that, for the flow of Newtonian fluid in annulus with the inner cylinder executing a planetary motion, the rotation and revolution velocities and the eccentricity are the main effects to the normal stress difference, tangential stress and moment acted on the inner cylinder, while the pressure gradient has no effect on them; for the flow of power law fluid in annulus with the inner cylinder executing a planetary motion, the rotation and revolution velocities and the eccentricity are the main effects to the normal stress difference, tangential stress and moment acted on the inner cylinder, while the pressure gradient has less effect on the normal stress difference and the tangential stress, and has much effect on the moment. Through the correlation analysis between the analytical solutions and the numerical solutions of the normal stress difference, tangential stress and moment acted on the inner cylinder, it is known that the calculation formulas and numerical calculation methods of the normal stress difference, tangential stress and moment acted on the inner cylinder by the fluid given in this paper are workable.By the distribution curves of the normal stress difference acted on the inner cylinder, under the behavior of production by screw pump, the normal stress difference distribution is found anti-symmetrical, meaning that there is radial force acted on the inner cylinder, which is the main factor of the problem of eccentric wear between the pump rod and the oil tube. In base of that, the technology of controlling eccentric wear in screw pump production well takes preferable impression in screw pump production wells of Oil Production Plant NO.6 of Daqing Oilfield. And by analyzing the tangential stress and the moment acted on the inner cylinder, the new theoretical bases could be provided for analyzing the forces acted on the pump rod and optimizing and designing the parameters of pump in screw pump production well.